In this post, we will look closely at a popular pose in Ballet, the Arabesque. We will do so from the perspective of Center of Mass as the Arabesque is a pose that requires proper balance in its execution.
Our analysis starts off with a deconstruction of the human body representing each of its parts in terms of line segments. The photo below shows a sketch of the Arabesque and a line segment deconstruction. For purposes of simplicity, we will keep our analysis in 2 dimensions. We will also assume the angle between the legs is 90 degrees and the angle between the trunk the vertical axis as 30 degrees. The standing leg is assumed to coincide with the vertical axis.
We will use representative data on a dancers body, taken from Tozeren, 1999.
The first step is to determine the positions of the segment midpoints with respect to the origin. Once this is determine, we the proceed to calculate the moment for each of the segment midpoints. A moment is the representative mass of the segment multiplied by the segment midpoint position. This is done for both vertical and horizontal coordinates. The moments are then totaled according to axis and divided by the total mass of the segments. These results in the coordinates of the center of mass.
Going back to our sketch, we find that the center of mass is 4cm away from the vertical axis which in this case is the center of support. This means the dancer will have to pull the body towards the arabesque leg to bring the body over the center of support. Another way of managing this is to work on the height of the Arabesque leg to move the center of mass toward the vertical.
To help the dancer improve balance in Arabesque, numerical simulations would be great sources of information to guide training. This will likely a subject in a future blog post.
Our analysis starts off with a deconstruction of the human body representing each of its parts in terms of line segments. The photo below shows a sketch of the Arabesque and a line segment deconstruction. For purposes of simplicity, we will keep our analysis in 2 dimensions. We will also assume the angle between the legs is 90 degrees and the angle between the trunk the vertical axis as 30 degrees. The standing leg is assumed to coincide with the vertical axis.
We will use representative data on a dancers body, taken from Tozeren, 1999.
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| Taken from Human Body Dynamics - Classical Mechanics and Human Movement by A. Tozeren, 1999 |
The first step is to determine the positions of the segment midpoints with respect to the origin. Once this is determine, we the proceed to calculate the moment for each of the segment midpoints. A moment is the representative mass of the segment multiplied by the segment midpoint position. This is done for both vertical and horizontal coordinates. The moments are then totaled according to axis and divided by the total mass of the segments. These results in the coordinates of the center of mass.
Going back to our sketch, we find that the center of mass is 4cm away from the vertical axis which in this case is the center of support. This means the dancer will have to pull the body towards the arabesque leg to bring the body over the center of support. Another way of managing this is to work on the height of the Arabesque leg to move the center of mass toward the vertical.
To help the dancer improve balance in Arabesque, numerical simulations would be great sources of information to guide training. This will likely a subject in a future blog post.
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